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Use the properties of logarithms to rewrite and simplify the logarithmic expression.ln2e5

Question

Use the properties of logarithms to rewrite and simplify the logarithmic expression.ln2e5

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Solution

The given expression is ln(2e^5).

Step 1: Apply the properties of logarithms. The logarithm of a product is the sum of the logarithms of its factors. So, we can rewrite the expression as follows:

ln(2e^5) = ln(2) + ln(e^5)

Step 2: Simplify the second term. The natural logarithm of e to the power of a number is just that number. So, ln(e^5) = 5.

So, the simplified expression is:

ln(2) + 5

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